From 64b9cc5d249a3c56824b46c3c9ec28fb2743c375 Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Tue, 11 Jun 2024 15:49:13 +0200 Subject: [PATCH 1/9] Added draft description of un-correlated symmetric sources with non-symmetric source model --- example/symmetry.md | 110 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 110 insertions(+) diff --git a/example/symmetry.md b/example/symmetry.md index e9151ac4c..addfecafe 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -9,6 +9,116 @@ When you expect symmetric activity in an ERP analysis, it makes sense to use a s This is especially beneficial when the source activity in left and right hemisphere is expected to be highly correlated, as the beamformer expects sources to be (reasonably) uncorrelated. By extending the sourcemodel, the source activity that you are simultaneously estimating while scanning includes both left and right hemisphere activity and the correlation _inside_ that sourcemodel is not a problem. +## Simulation of correlated and un-correlated symmetric dipole pairs + +To investigate the effects of applying a symmetry constraint to the beamformer analysis, we will simulate two scenarios of symmetric dipoles; correlated and un-correlated. We will then attempt to estimate them with and without symmetry constraints. +First, the symmetric dipoles and a spherical volume conducter model are defined: + + % Define two dipole positions and two directions of moment + dippos = [-4 -4 4; 4 -4 4]; + dipmom = [1 0 .5; -1 0 .5]'; + + % Create an array with some magnetometers at 12cm distance from the origin + [X, Y, Z] = sphere(10); + pos = unique([X(:) Y(:) Z(:)], 'rows'); + pos = pos(pos(:,3)>=0,:); + grad = []; + grad.coilpos = 12*pos; + grad.coilori = pos; % in the outward direction + + for i=1:length(pos) + grad.label{i} = sprintf('chan%03d', i); + end + + % Create a spherical volume conductor with 10cm radius + vol.r = 10; + vol.o = [0 0 0]; + +Then, two source models are defined; a 'normal' non-symmetric model and one with the symmetry constraint defined for the x-axis (which in this case defines the 'midline'): + + % Source models are defined with x-axis normal to the midline. + % Non-symmetric 'normal' source model + cfg = []; + cfg.headmodel = vol; % use the spherical volume conducter as head model + cfg.grad = grad; + cfg.xgrid = -9.5:9.5; % ensure that the midline is not included + cfg.ygrid = -10:10; + cfg.zgrid = 0:10; + sourcemodel_normal = ft_prepare_leadfield(cfg); + + % Source model with symmetry constraint over the midline. + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.xgrid = -9.5:0; % ensure that the midline is not included + cfg.ygrid = -10:10; + cfg.zgrid = 0:10; + cfg.symmetry = 'x'; + sourcemodel_double = ft_prepare_leadfield(cfg); + + % Plot the grids of the two models + figure + ft_plot_mesh(sourcemodel_normal.pos(sourcemodel_normal.inside,:)) + ft_plot_sens(grad) + + figure + ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,1:3), 'vertexcolor', 'r') + ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,4:6), 'vertexcolor', 'b') + ft_plot_sens(grad) + +{% include image src="/assets/img/example/symmetry/sourcemodel_normal.png" width="300" %} +{% include image src="/assets/img/example/symmetry/sourcemodel_double.png" width="300" %} + +In the symmetric sourcemodel, the `.pos` field is evidently a `N/2x6` matrix (where `N` is the number of vertices in the grid), rather than the usual `Nx3`, where the xyz-coordinates of the vertices are given in pairs of triplets. + +### Un-correlated symmetric sources with non-symmetric source model + +We now define two conditions with uncorrelated (i.e. phase shifted) symmetric 40~Hz signals of varying amplitude emulating a left and right lateral attention modulation: + + cfg.sourcemodel.pos = dippos(:,:); + cfg.sourcemodel.mom = dipmom(:,:); + % create some left-right amplitude imbalance, emulating lateral attention modulation + cfg.sourcemodel.signal = repmat({[1.1*sin(40*2*pi*(0:999)/1000); 0.9*cos(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attL = ft_dipolesimulation(cfg); + cfg.sourcemodel.signal = repmat({[0.9*sin(40*2*pi*(0:999)/1000); 1.1*cos(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attR = ft_dipolesimulation(cfg); + + +Compute the data covariance matrix, which will capture the activity of each simulated dipole and is needed for the beamformer source estimation: + + cfg = []; + cfg.covariance = 'yes'; + timelockLR_attL = ft_timelockanalysis(cfg, dataLR_attL); + timelockLR_attR = ft_timelockanalysis(cfg, dataLR_attR); + +Now, apply the beamformer based on the non-symmetric 'normal' source model, calculate the lateral contrast, and plot the result: + + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.sourcemodel = sourcemodel_normal; + cfg.method = 'lcmv'; + singleLR_attL = ft_sourceanalysis(cfg, timelockLR_attL); + singleLR_attR = ft_sourceanalysis(cfg, timelockLR_attR); + + cfg = []; + cfg.operation = '(x2-x1)/(x1+x2)'; % right minus left + cfg.parameter = 'pow'; + contrastLR_attL_attR = ft_math(cfg, singleLR_attL, singleLR_attR); + + cfg = []; + cfg.method = 'slice'; + cfg.funparameter = 'pow'; + figure; ft_sourceplot(cfg, contrastLR_attL_attR); + +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR.png" width="300" %} + +### Correlated symmetric sources with non-symmetric source model + + + +## Example auditory steady state response + {% include markup/yellow %} This is explained for Steady State Auditory Potentials (SSAEPs) in the paper by Tzvetan Popov, Robert Oostenveld, Jan M. Schoffelen (2018) [FieldTrip Made Easy: An Analysis Protocol for Group Analysis of the Auditory Steady State Brain Response in Time, Frequency, and Space](https://doi.org/10.3389/fnins.2018.00711). Supporting material, including all data and scripts can be found on the [Radboud Data Repository](https://doi.org/10.34973/fkgz-8d22). From bc57aea96e85b7b6279b1cd4da53be12eb64bceb Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Tue, 11 Jun 2024 15:52:16 +0200 Subject: [PATCH 2/9] Add remaining headers --- example/symmetry.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/example/symmetry.md b/example/symmetry.md index addfecafe..29a49e3f3 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -115,7 +115,9 @@ Now, apply the beamformer based on the non-symmetric 'normal' source model, calc ### Correlated symmetric sources with non-symmetric source model +### Un-correlated symmetric sources with symmetric source model +### Correlated symmetric sources with non-symmetric source model ## Example auditory steady state response From ca45377dc07d4509ddc903d47bf09c184e554d41 Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Tue, 11 Jun 2024 16:03:01 +0200 Subject: [PATCH 3/9] Add correlated sources with non-symmetric source model --- example/symmetry.md | 43 +++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 41 insertions(+), 2 deletions(-) diff --git a/example/symmetry.md b/example/symmetry.md index 29a49e3f3..98b91fa08 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -83,7 +83,6 @@ We now define two conditions with uncorrelated (i.e. phase shifted) symmetric 40 cfg.sourcemodel.signal = repmat({[0.9*sin(40*2*pi*(0:999)/1000); 1.1*cos(40*2*pi*(0:999)/1000)]}, 1, 10); dataLR_attR = ft_dipolesimulation(cfg); - Compute the data covariance matrix, which will capture the activity of each simulated dipole and is needed for the beamformer source estimation: cfg = []; @@ -111,12 +110,52 @@ Now, apply the beamformer based on the non-symmetric 'normal' source model, calc cfg.funparameter = 'pow'; figure; ft_sourceplot(cfg, contrastLR_attL_attR); -{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR.png" width="300" %} +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_uncor.png" width="300" %} ### Correlated symmetric sources with non-symmetric source model +Now, let's make the oscillations of the two symmetric dipoles correlated by changing the right dipole signals from cosines to sines: + + cfg.sourcemodel.pos = dippos(:,:); + cfg.sourcemodel.mom = dipmom(:,:); + % create some left-right amplitude imbalance, emulating lateral attention modulation. + % OBS: Notice the right dipole signal is now also defined by a sine + cfg.sourcemodel.signal = repmat({[1.1*sin(40*2*pi*(0:999)/1000); 0.9*sin(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attL = ft_dipolesimulation(cfg); + cfg.sourcemodel.signal = repmat({[0.9*sin(40*2*pi*(0:999)/1000); 1.1*sin(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attR = ft_dipolesimulation(cfg); + +We then compute the covariance and apply the beamformer still with the non-symetric source model: + + cfg = []; + cfg.covariance = 'yes'; + timelockLR_attL = ft_timelockanalysis(cfg, dataLR_attL); + timelockLR_attR = ft_timelockanalysis(cfg, dataLR_attR); + + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.sourcemodel = sourcemodel_normal; + cfg.method = 'lcmv'; + singleLR_attL = ft_sourceanalysis(cfg, timelockLR_attL); + singleLR_attR = ft_sourceanalysis(cfg, timelockLR_attR); + + cfg = []; + cfg.operation = '(x2-x1)/(x1+x2)'; % right minus left + cfg.parameter = 'pow'; + contrastLR_attL_attR = ft_math(cfg, singleLR_attL, singleLR_attR); + + cfg = []; + cfg.method = 'slice'; + cfg.funparameter = 'pow'; + figure; ft_sourceplot(cfg, contrastLR_attL_attR); + +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_cor.png" width="300" %} + ### Un-correlated symmetric sources with symmetric source model + + ### Correlated symmetric sources with non-symmetric source model ## Example auditory steady state response From d1c7f8e4bb6d5afc384f75e753315d5c94d6df47 Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Wed, 12 Jun 2024 14:35:25 +0200 Subject: [PATCH 4/9] Add complete draft of symmetry sim tutourial --- example/symmetry.md | 236 ++++++++++++++++++++++++++++++++++++++------ 1 file changed, 207 insertions(+), 29 deletions(-) diff --git a/example/symmetry.md b/example/symmetry.md index 98b91fa08..c70294f50 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -11,7 +11,8 @@ This is especially beneficial when the source activity in left and right hemisph ## Simulation of correlated and un-correlated symmetric dipole pairs -To investigate the effects of applying a symmetry constraint to the beamformer analysis, we will simulate two scenarios of symmetric dipoles; correlated and un-correlated. We will then attempt to estimate them with and without symmetry constraints. +To investigate the effects of applying a symmetry constraint to the beamformer analysis, we will simulate two scenarios of symmetric dipoles; correlated and un-correlated. We will then attempt to estimate them with and without symmetry constraints. There coherent simulation script is available **[here](https://github.com/henneysq/meg-ahat/blob/main/simulations/symmetric_dipoles_tutorial.m)**. + First, the symmetric dipoles and a spherical volume conducter model are defined: % Define two dipole positions and two directions of moment @@ -34,47 +35,37 @@ First, the symmetric dipoles and a spherical volume conducter model are defined: vol.r = 10; vol.o = [0 0 0]; -Then, two source models are defined; a 'normal' non-symmetric model and one with the symmetry constraint defined for the x-axis (which in this case defines the 'midline'): +Then, a 'normal' non-symmetric source model is defined, and the grid is plotted: - % Source models are defined with x-axis normal to the midline. - % Non-symmetric 'normal' source model + % Define a non-symmetric 'normal' source model cfg = []; cfg.headmodel = vol; % use the spherical volume conducter as head model cfg.grad = grad; + % Source models are defined with x-axis normal to the midline. cfg.xgrid = -9.5:9.5; % ensure that the midline is not included cfg.ygrid = -10:10; cfg.zgrid = 0:10; sourcemodel_normal = ft_prepare_leadfield(cfg); - % Source model with symmetry constraint over the midline. - cfg = []; - cfg.headmodel = vol; - cfg.grad = grad; - cfg.xgrid = -9.5:0; % ensure that the midline is not included - cfg.ygrid = -10:10; - cfg.zgrid = 0:10; - cfg.symmetry = 'x'; - sourcemodel_double = ft_prepare_leadfield(cfg); - - % Plot the grids of the two models + % Plot the grid of the source model figure ft_plot_mesh(sourcemodel_normal.pos(sourcemodel_normal.inside,:)) ft_plot_sens(grad) - figure - ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,1:3), 'vertexcolor', 'r') - ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,4:6), 'vertexcolor', 'b') - ft_plot_sens(grad) - -{% include image src="/assets/img/example/symmetry/sourcemodel_normal.png" width="300" %} -{% include image src="/assets/img/example/symmetry/sourcemodel_double.png" width="300" %} +{% include image src="/assets/img/example/symmetry/sourcemodel_normal.png" width="600" %} -In the symmetric sourcemodel, the `.pos` field is evidently a `N/2x6` matrix (where `N` is the number of vertices in the grid), rather than the usual `Nx3`, where the xyz-coordinates of the vertices are given in pairs of triplets. +--- ### Un-correlated symmetric sources with non-symmetric source model -We now define two conditions with uncorrelated (i.e. phase shifted) symmetric 40~Hz signals of varying amplitude emulating a left and right lateral attention modulation: +Two conditions are defined with uncorrelated (i.e. phase shifted) symmetric 40 Hz signals of varying amplitude emulating a left and right lateral attention modulation. Note that the left dipole signal is defined by a sin while the right is defined by a cos. + % Dipole simulation + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.fsample = 1000; + cfg.relnoise = 2; cfg.sourcemodel.pos = dippos(:,:); cfg.sourcemodel.mom = dipmom(:,:); % create some left-right amplitude imbalance, emulating lateral attention modulation @@ -90,7 +81,7 @@ Compute the data covariance matrix, which will capture the activity of each simu timelockLR_attL = ft_timelockanalysis(cfg, dataLR_attL); timelockLR_attR = ft_timelockanalysis(cfg, dataLR_attR); -Now, apply the beamformer based on the non-symmetric 'normal' source model, calculate the lateral contrast, and plot the result: +Apply the beamformer based on the non-symmetric 'normal' source model, calculate the lateral contrast, and plot the result: cfg = []; cfg.headmodel = vol; @@ -110,12 +101,20 @@ Now, apply the beamformer based on the non-symmetric 'normal' source model, calc cfg.funparameter = 'pow'; figure; ft_sourceplot(cfg, contrastLR_attL_attR); -{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_uncor.png" width="300" %} +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_uncor.png" width="600" %} + +--- ### Correlated symmetric sources with non-symmetric source model Now, let's make the oscillations of the two symmetric dipoles correlated by changing the right dipole signals from cosines to sines: + % Dipole simulation + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.fsample = 1000; + cfg.relnoise = 2; cfg.sourcemodel.pos = dippos(:,:); cfg.sourcemodel.mom = dipmom(:,:); % create some left-right amplitude imbalance, emulating lateral attention modulation. @@ -125,7 +124,7 @@ Now, let's make the oscillations of the two symmetric dipoles correlated by chan cfg.sourcemodel.signal = repmat({[0.9*sin(40*2*pi*(0:999)/1000); 1.1*sin(40*2*pi*(0:999)/1000)]}, 1, 10); dataLR_attR = ft_dipolesimulation(cfg); -We then compute the covariance and apply the beamformer still with the non-symetric source model: +Compute the covariance and apply the beamformer still with the non-symetric source model: cfg = []; cfg.covariance = 'yes'; @@ -150,13 +149,192 @@ We then compute the covariance and apply the beamformer still with the non-symet cfg.funparameter = 'pow'; figure; ft_sourceplot(cfg, contrastLR_attL_attR); -{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_cor.png" width="300" %} +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_nonsym_cor.png" width="600" %} + +Due to the correlation between the spatially seperated source signals, the LCMV estimator produces a sub-optimal spatial filter that is less sensitive to both sources. + +--- + +### Correlated symmetric sources with symmetric source model + +To deal with the correlation between the symmetric dipoles, the source model is re-defined with a symmetry constraint across the midline (in this case the x-axis): + + % Source model with symmetry constraint over the midline. + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.xgrid = -9.5:0; % Only define one hemisphere + cfg.ygrid = -10:10; + cfg.zgrid = 0:10; + cfg.symmetry = 'x'; % Axis of symmetry - OBS: This is dependent on scanner coordinate system + sourcemodel_double = ft_prepare_leadfield(cfg); + +In the symmetric sourcemodel, the `.pos` field is a `N/2x6` matrix (where `N` is the number of vertices in the grid), rather than the usual `Nx3`, where the xyz-coordinates of the vertices are given in pairs of triplets. + + sourcemodel_double.pos + ans = + +Plot the symmetrically defined grid, colour coding each hemisphere: + + figure + ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,1:3), 'vertexcolor', 'r') + ft_plot_mesh(sourcemodel_double.pos(sourcemodel_double.inside,4:6), 'vertexcolor', 'b') + ft_plot_sens(grad) + +{% include image src="/assets/img/example/symmetry/sourcemodel_double.png" width="600" %} + +Re-do the beamformer estimation with the symmetric source model + + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.sourcemodel = sourcemodel_double; + cfg.method = 'lcmv'; + singleLR_attL = ft_sourceanalysis(cfg, timelockLR_attL); + singleLR_attR = ft_sourceanalysis(cfg, timelockLR_attR); + +Now, the source estimates need to be reshaped from the symmetrically defined source model to the normal source model dimensions: + + % construct the single-dipole model from the (symmetric) double-dipole model + n = size(sourcemodel_double.pos,1); + lh2full = nan(n,1); + rh2full = nan(n,1); + + % determine the mapping between the left and right hemisphere to the full model + for i=1:n + pos_lh = sourcemodel_double.pos(i,1:3); % Left hemisphere positions + pos_rh = sourcemodel_double.pos(i,4:6); % Right hemisphere positions + lh2full(i) = find(sourcemodel_normal.pos(:,1)==pos_lh(1) & sourcemodel_normal.pos(:,2)==pos_lh(2) & sourcemodel_normal.pos(:,3)==pos_lh(3)); + rh2full(i) = find(sourcemodel_normal.pos(:,1)==pos_rh(1) & sourcemodel_normal.pos(:,2)==pos_rh(2) & sourcemodel_normal.pos(:,3)==pos_rh(3)); + end + + % this mainly serves as a sanity check + sourcemodel_single = []; + sourcemodel_single.pos(lh2full, 1) = sourcemodel_double.pos(:,1); + sourcemodel_single.pos(lh2full, 2) = sourcemodel_double.pos(:,2); + sourcemodel_single.pos(lh2full, 3) = sourcemodel_double.pos(:,3); + sourcemodel_single.pos(rh2full, 1) = sourcemodel_double.pos(:,4); + sourcemodel_single.pos(rh2full, 2) = sourcemodel_double.pos(:,5); + sourcemodel_single.pos(rh2full, 3) = sourcemodel_double.pos(:,6); + + % these should now be equal + assert(isequal(sourcemodel_single.pos, sourcemodel_normal.pos)); + + sourcemodel_single.dim = sourcemodel_normal.dim; + sourcemodel_single.unit = sourcemodel_normal.unit; + sourcemodel_single.inside = sourcemodel_normal.inside; + + % convert the (symmetric) double-dipole estimates into a single-dipole representation + singleLR_attL = sourcemodel_single; + singleLR_attL.pow = nan(prod(sourcemodel_normal.dim),1); + singleLR_attR = sourcemodel_single; + singleLR_attR.pow = nan(prod(sourcemodel_normal.dim),1); + +Extract the covariance from each hemisphere and calculate the power using the first singular value: + + for i=find(doubleLR_attL.inside(:)') + covL = doubleLR_attL.avg.cov{i}(1:3,1:3); % Left hemisphere covariance + covR = doubleLR_attL.avg.cov{i}(4:6,4:6); % Right hemisphere covariance + powL = svd(covL); powL = powL(1); % Estimate power by 1st singular value + powR = svd(covR); powR = powR(1); + singleLR_attL.pow(lh2full(i)) = powL; + singleLR_attL.pow(rh2full(i)) = powR; + + covL = doubleLR_attR.avg.cov{i}(1:3,1:3); + covR = doubleLR_attR.avg.cov{i}(4:6,4:6); + powL = svd(covL); powL = powL(1); + powR = svd(covR); powR = powR(1); + singleLR_attR.pow(lh2full(i)) = powL; + singleLR_attR.pow(rh2full(i)) = powR; + end + +Compute the contrast between the conditions as before and plot the results + + cfg = []; + cfg.operation = '(x2-x1)/(x1+x2)'; % right minus left + cfg.parameter = 'pow'; + contrastLR_attL_attR = ft_math(cfg, singleLR_attL, singleLR_attR); + + cfg = []; + cfg.method = 'slice'; + cfg.funparameter = 'pow'; + figure; ft_sourceplot(cfg, contrastLR_attL_attR); + +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_sym_cor.png" width="600" %} + +--- ### Un-correlated symmetric sources with symmetric source model +Finally, we show the effect of using a symmetric source model to estimate two un-correlated symmetric sources: -### Correlated symmetric sources with non-symmetric source model + % Dipole simulation + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.fsample = 1000; + cfg.relnoise = 2; + cfg.sourcemodel.pos = dippos(:,:); + cfg.sourcemodel.mom = dipmom(:,:); + % create some left-right amplitude imbalance, emulating lateral attention modulation. + % OBS: Notice the right dipole signal is now also defined by a sine + cfg.sourcemodel.signal = repmat({[1.1*sin(40*2*pi*(0:999)/1000); 0.9*cos(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attL = ft_dipolesimulation(cfg); + cfg.sourcemodel.signal = repmat({[0.9*sin(40*2*pi*(0:999)/1000); 1.1*cos(40*2*pi*(0:999)/1000)]}, 1, 10); + dataLR_attR = ft_dipolesimulation(cfg); + + % Compute covariance + cfg = []; + cfg.covariance = 'yes'; + timelockLR_attL = ft_timelockanalysis(cfg, dataLR_attL); + timelockLR_attR = ft_timelockanalysis(cfg, dataLR_attR); + + % Do symmetric source estimation + cfg = []; + cfg.headmodel = vol; + cfg.grad = grad; + cfg.sourcemodel = sourcemodel_double; + cfg.method = 'lcmv'; + singleLR_attL = ft_sourceanalysis(cfg, timelockLR_attL); + singleLR_attR = ft_sourceanalysis(cfg, timelockLR_attR); + + % convert the (symmetric) double-dipole estimates into a single-dipole representation + singleLR_attL = sourcemodel_single; + singleLR_attL.pow = nan(prod(sourcemodel_normal.dim),1); + singleLR_attR = sourcemodel_single; + singleLR_attR.pow = nan(prod(sourcemodel_normal.dim),1); + + % Extract the covariance from each hemisphere and calculate the power using the first singular value: + for i=find(doubleLR_attL.inside(:)') + covL = doubleLR_attL.avg.cov{i}(1:3,1:3); % Left hemisphere covariance + covR = doubleLR_attL.avg.cov{i}(4:6,4:6); % Right hemisphere covariance + powL = svd(covL); powL = powL(1); % Estimate power by 1st singular value + powR = svd(covR); powR = powR(1); + singleLR_attL.pow(lh2full(i)) = powL; + singleLR_attL.pow(rh2full(i)) = powR; + + covL = doubleLR_attR.avg.cov{i}(1:3,1:3); + covR = doubleLR_attR.avg.cov{i}(4:6,4:6); + powL = svd(covL); powL = powL(1); + powR = svd(covR); powR = powR(1); + singleLR_attR.pow(lh2full(i)) = powL; + singleLR_attR.pow(rh2full(i)) = powR; + end + + % Compute contrast + cfg = []; + cfg.operation = '(x2-x1)/(x1+x2)'; % right minus left + cfg.parameter = 'pow'; + contrastLR_attL_attR = ft_math(cfg, singleLR_attL, singleLR_attR); + + % Plot source contrasts + cfg = []; + cfg.method = 'slice'; + cfg.funparameter = 'pow'; + figure; ft_sourceplot(cfg, contrastLR_attL_attR); + +{% include image src="/assets/img/example/symmetry/contrastLR_attL_attR_sym_uncor.png" width="600" %} ## Example auditory steady state response From 0bd1d9597afb1b6e98875016712791f2f5a701aa Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Wed, 12 Jun 2024 14:35:58 +0200 Subject: [PATCH 5/9] add initial image assets --- .../contrastLR_attL_attR_nonsym_cor.png | Bin 0 -> 21428 bytes .../contrastLR_attL_attR_nonsym_uncor.png | Bin 0 -> 19334 bytes .../symmetry/contrastLR_attL_attR_sym_cor.png | Bin 0 -> 23194 bytes .../img/example/symmetry/sourcemodel_double.png | Bin 0 -> 9465 bytes .../img/example/symmetry/sourcemodel_normal.png | Bin 0 -> 8333 bytes 5 files changed, 0 insertions(+), 0 deletions(-) create mode 100755 assets/img/example/symmetry/contrastLR_attL_attR_nonsym_cor.png create mode 100755 assets/img/example/symmetry/contrastLR_attL_attR_nonsym_uncor.png create mode 100755 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zFf5%{_#;)P`?$@`s6d{i6Ql1fEKt0nddZQ2&#G{=FENLJ+|M{(3pcm62v)}ls6IK^ zuG|2itoj4a2MG3`8fd^*5_bi`GErN==JI*7l55=&faCc;bHf8~=n#n34a+@h$> zvrES&m{wtiWE5HZ(n$(&NRYC!Mz*XNnmE6QsCAMi;{v(-`ss-0c|gd<@b=z;!>qC? zVVu8nz1gNSfR?ZOXsxa_+rHWe1X<`m)c@QqD$I_@0H|%+IYH33HOqY@)wp? otNk5q|9AAyx#xegHTIZ`=(*l8cL)Ju5(s2sXl_uc=X~$~0e&V?_W%F@ diff --git a/assets/img/example/symmetry/sourcemodel_normal.png b/assets/img/example/symmetry/sourcemodel_normal.png index 08236e873e0d199a41b2418fb059c584a26eaf4e..e478f00f7f3bfa302fff0332698a1ef4c353f1a3 100755 GIT binary patch delta 33 pcmeBm>~);r#LmYqc*p8d#zfCxZZj(bb1OshnqR%~8<#(m2LQm$3~T@Z delta 33 pcmeBm>~);r#Lg+gWTWzB;Y811ZbK_011kd~b8FdS8<#(m2LP=Y3f%wz From b322875d3ca215cd0e5ec5b9f5053a5de784d99f Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Wed, 12 Jun 2024 16:19:33 +0200 Subject: [PATCH 7/9] add head of .pos printout --- example/symmetry.md | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) diff --git a/example/symmetry.md b/example/symmetry.md index c70294f50..0097c94cf 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -171,8 +171,15 @@ To deal with the correlation between the symmetric dipoles, the source model is In the symmetric sourcemodel, the `.pos` field is a `N/2x6` matrix (where `N` is the number of vertices in the grid), rather than the usual `Nx3`, where the xyz-coordinates of the vertices are given in pairs of triplets. - sourcemodel_double.pos - ans = + >> head(sourcemodel_double.pos) + -9.5000 -9.0000 0 9.5000 -9.0000 0 + -8.5000 -9.0000 0 8.5000 -9.0000 0 + -7.5000 -9.0000 0 7.5000 -9.0000 0 + -6.5000 -9.0000 0 6.5000 -9.0000 0 + -5.5000 -9.0000 0 5.5000 -9.0000 0 + -4.5000 -9.0000 0 4.5000 -9.0000 0 + -3.5000 -9.0000 0 3.5000 -9.0000 0 + -2.5000 -9.0000 0 2.5000 -9.0000 0 Plot the symmetrically defined grid, colour coding each hemisphere: From ddeaada13db59f26281a23d114e833d56dd62fc5 Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Fri, 14 Jun 2024 10:30:31 +0200 Subject: [PATCH 8/9] add symmetry tag --- example/symmetry.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/example/symmetry.md b/example/symmetry.md index 0097c94cf..83c12aff2 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -1,6 +1,6 @@ --- title: Symmetric dipole pairs for beamforming -tags: [example, source] +tags: [example, source, symmetry] --- # Symmetric dipole pairs for beamforming From 5ca8868a1721965841e5da90faa3a2ca77118769 Mon Sep 17 00:00:00 2001 From: Mark Henney Date: Fri, 14 Jun 2024 12:01:42 +0200 Subject: [PATCH 9/9] Add code exerpts from Popov2028 --- example/symmetry.md | 177 ++++++++++++++++++++++++++++++++++---------- 1 file changed, 137 insertions(+), 40 deletions(-) diff --git a/example/symmetry.md b/example/symmetry.md index 83c12aff2..cb21cfbbb 100644 --- a/example/symmetry.md +++ b/example/symmetry.md @@ -346,56 +346,153 @@ Finally, we show the effect of using a symmetric source model to estimate two un ## Example auditory steady state response {% include markup/yellow %} -This is explained for Steady State Auditory Potentials (SSAEPs) in the paper by Tzvetan Popov, Robert Oostenveld, Jan M. Schoffelen (2018) [FieldTrip Made Easy: An Analysis Protocol for Group Analysis of the Auditory Steady State Brain Response in Time, Frequency, and Space](https://doi.org/10.3389/fnins.2018.00711). Supporting material, including all data and scripts can be found on the [Radboud Data Repository](https://doi.org/10.34973/fkgz-8d22). +The use of symmetric dipoles is explained for Steady State Auditory Potentials (SSAEPs) in the paper by Tzvetan Popov, Robert Oostenveld, Jan M. Schoffelen (2018) [FieldTrip Made Easy: An Analysis Protocol for Group Analysis of the Auditory Steady State Brain Response in Time, Frequency, and Space](https://doi.org/10.3389/fnins.2018.00711). Supporting material, including all data and scripts can be found on the [Radboud Data Repository](https://doi.org/10.34973/fkgz-8d22). {% include badge doi="10.3389/fnins.2018.00711" pmid="30356712" pmcid="PMC6189392" %} {% include markup/end %} +The following exerpts from [`ASSR_dics.m` (download)](https://data.ru.nl/api/di/downloadFiles/download?filePath=analysis_scripts%2FASSR_dics.m&versionId=di_44792555) make up the analysis pipeline of the SSAEPs from [Popov et. al. 2018](https://doi.org/10.3389/fnins.2018.00711) using symmetric dipoles and [Dynamic imaging of coherent sources](https://doi.org/10.1073/pnas.98.2.694) (DICS). The SSAEP is a very high SNR signal, leading to (near) simultaneous (i.e. zero-lag correlated) activation in bilateral auditory areas. Therefore, the traditional beamformer will fail to yield good results. Note that the exerpts present the method on a single subject, while `ASSR_dics.m` provide analysis accross subjects as well. + +Configure data and FieldTrip paths, and specify some study metadata: + + % initialize fieldtrip + path_ft = '/path/to/fieldtrip'; + path_data = '/path/to/data/ASSR'; + + % this adds fieldtrip to the matlab path + the relevant subdirectories + addpath(path_ft); + ft_defaults; + + % we choose a single subject for demonstration purposes + subject = '45048' + +Load in the precomputed geometric data that is needed for source +reconstruction: the forward model (leadfields), as well as the volume +conductor model of the head, and the electrodes. Strictly speaking, once +the forward model is available, the other objects are not needed anymore, +but FieldTrip expects them to be present in the cfg. + + load(fullfile(path_data,'templates','headmodel.mat')); + load(fullfile(path_data,'templates','leadfield.mat')); + load(fullfile(path_data,'templates','elec_aligned.mat')); + +In this example here, we have already computed leadfields, +so we will create for each original dipole location a leadfield +consisting of a concatenation of this dipole's leadfield with its +counterpart in the opposite hemisphere. Note that the x-coordinate here +is the left/right direction. + + lf1 = reshape(leadfield.leadfield, leadfield.dim); + lf2 = flip(lf1,1); + for k = 1:numel(lf1) + if ~isempty(lf1{k})&&~isempty(lf2{k}) + leadfield.leadfield{k} = [lf1{k} lf2{k}]; + else + leadfield.leadfield{k} = []; + leadfield.inside(k) = false; + end + end + clear lf1 lf2 - mri = ft_read_mri('Subject01.mri'); - - % just to check that it is in CTF coordinates and that the y axis is from right (-y) to left (+y) - ft_determine_coordsys(mri, 'interactive', false) +Load the data and divide it into pre and post stimulus segments. We also concatenate the two for the purpose of estimating a common spatial filter. - % we only need the brain surface, as we'll use a singleshell MEG volume conductor - cfg = []; - cfg.output = {'brain'}; - cfg.spmmethod = 'new'; - cfg.spmversion = 'spm12'; - mri_segmented = ft_volumesegment(cfg, mri); + datafile = fullfile(path_data, 'data', subject, 'data.mat'); + load(datafile) - cfg = []; - cfg.method = 'singleshell'; - headmodel = ft_prepare_headmodel(cfg, mri_segmented); + % remove bad channels + cfg = []; + cfg.channel = {'all' '-E30' '-E3' '-E4' '-E11' '-E12' '-Cz' '-E192'}; + data = ft_selectdata(cfg, data); + + % this chunk of code creates a 'dummy' reference channel to be used for + % the coherence analysis + trial = cell(size(data.trial)); + for k = 1:numel(trial) + trial{k} = sin(2.*pi.*40.*data.time{k}); + end + refdata.trial = trial; + refdata.time = data.time; + refdata.label = {'refchan'}; + data = ft_appenddata([], data, refdata); + data.fsample = 1000; + + % re-segment the data into pre and post stimulus onset intervals + cfg = []; + cfg.toilim = [-1 0-1./data.fsample]; + datapre = ft_redefinetrial(cfg, data); + + cfg.toilim = [1 2-1./data.fsample]; + datapost = ft_redefinetrial(cfg, data); - % just to be sure, since we'll specify numbers further down - headmodel = ft_convert_units(headmodel, 'mm'); + % append data to facilitate the computation of a 'common' spatial filter + dataall = ft_appenddata([], datapre, datapost); - cfg = []; - cfg.headmodel = headmodel; - cfg.symmetry = 'y'; - cfg.xgrid = -150:10:150; % in mm - cfg.ygrid = 5:10:150; % in mm, one hemisphere, offset to the midline - cfg.zgrid = -150:10:150; % in mm - sourcemodel = ft_prepare_sourcemodel(cfg); - - % the source position is specified as 1547x6 - % corresponding to 1547 dipole pairs +The cross-spectral density matrices are calculated for each of the two conditions and the concatenated data. Here, we focus on the 40 Hz component: - % using the sensor description from the corresponding MEG data - % we can now compute the leadfields - grad = ft_read_sens('Subject01.ds', 'senstype', 'meg'); + cfg = []; + cfg.method = 'mtmfft'; + cfg.output = 'fourier'; + cfg.taper = 'hanning'; + cfg.foilim = [40 40]; + freqpre = ft_freqanalysis(cfg, datapre); + freqpost = ft_freqanalysis(cfg, datapost); + freqall = ft_freqanalysis(cfg, dataall); + + % the data consists of fewer channels than the precomputed + % leadfields, the following chunk of code takes care of this + [a,b] = match_str(data.label, leadfield.label); + for k = 1:numel(leadfield.leadfield) + if ~isempty(leadfield.leadfield{k}) + tmp = leadfield.leadfield{k}; + tmp = tmp(b,:); + tmp = tmp-repmat(mean(tmp,1),[size(tmp,1) 1]); % average re-ref + leadfield.leadfield{k} = tmp; + end + end + leadfield.label = leadfield.label(b); + +Perform source reconstruction using the DICS method . Note that `cfg.dics.keepfilter = 'yes'` allows us to pass the estimated spatial filter to the subsequent source analysis of individual conditions. + + cfg = []; + cfg.method = 'dics'; + cfg.frequency = 40; + cfg.channel = data.label; + cfg.elec = elec_aligned; + cfg.grid = leadfield; + cfg.headmodel = headmodel; + cfg.dics.keepfilter = 'yes'; + cfg.dics.fixedori = 'no'; + cfg.dics.projectnoise = 'yes'; + cfg.dics.lambda = '5%'; + cfg.dics.realfilter = 'yes'; + cfg.dics.keepcsd = 'yes'; + cfg.refchan = {'refchan'}; + sourceall = ft_sourceanalysis(cfg, freqall); + + % apply common filters to pre and post stimulus data + cfg.grid.filter = sourceall.avg.filter; + +Now we need to extract the dipole pairs' full csd matrix with respect to the reference channel, which is not possible in the traditional DICS implementation, but can be achieved with PCC - cfg = []; - cfg.grad = grad; - cfg.channel = {'MEGGRAD'}; - cfg.headmodel = headmodel; - cfg.sourcemodel = sourcemodel; - leadfield = ft_prepare_leadfield(cfg); + cfg.method = 'pcc'; + cfg = rmfield(cfg, 'dics'); + sourcepre = ft_sourceanalysis(cfg, freqpre); + sourcepst = ft_sourceanalysis(cfg, freqpost); + +Now we need to adjust the 'csdlabel', in order to compute the single dipole-of-interest coherence with the reference. source.avg.csd contains for each dipole pair the cross-spectral density as a 7x7 matrix, two triplets of rows/columns for each of the dipoles in the pair, and one for the reference signal. **[ft_sourcedescriptives](https://github.com/fieldtrip/fieldtrip/blob/master/ft_sourcedescriptives.m)** will return the coherence between the 'scandip' and the 'refchan', so we need to relabel the second dipole's label - % each leadfield matrix is 6x151, where 6 corresponds to 3 orientations for - % the dipole in left and 3 orientations for the dipole in the right hemisphere + for k = 1:size(sourcepre.pos,1) + if ~isempty(sourcepre.avg.csdlabel{k}) + sourcepre.avg.csdlabel{k}(4:6) = {'supdip'}; + sourcepst.avg.csdlabel{k}(4:6) = {'supdip'}; + end + end + sourcepre = ft_sourcedescriptives([], sourcepre); + sourcepst = ft_sourcedescriptives([], sourcepst); + +Contrast post stimulus onset activity with respect to baseline - figure - ft_plot_mesh(leadfield.pos(leadfield.inside, 1:3), 'vertexcolor', 'r') - ft_plot_mesh(leadfield.pos(leadfield.inside, 4:6), 'vertexcolor', 'b') + cfg = []; + cfg.operation = 'x2-x1'; + cfg.parameter = 'avg.coh'; + source_dics = ft_math(cfg,sourcepre,sourcepst); \ No newline at end of file